Through-bond and through-space interactions between nitrogen lone pairs are studied using ab initio methods for a series of symmetric bicyclic diamines with up to four -CH2- units in each bridge and for the molecules obtained by removing one and two of the methylene bridges. In all cases there are contributions to the odd-even splitting DELTA = epsilon(n-) - epsilon(n+) from through-space as well as through-bond interactions with a tendency for cancellation. The dependence of \DELTA\ on the number of bonds of the bridge is nonexponential at least for short bridges. For 1,4-diazabicyclo[2.2.2]octane and diethylenediamine the through-bond interactions dominate, giving a final (and large) negative DELTA. Correlation effects, particularly of polarization type, are studied and found to be quite significant.